The self consistency principle was developed by professor Novikov to solve the problem of paradoxes in time travel. It states that if an event could exist that will give rise to a paradox,then the probability of that event actually happening is zero. To demonstrate this theory he used a mathematical example
Imagine a billiard ball being fired into a wormhole in such a way, that it would go back in time and collide with its earlier self, thereby knocking it off course and preventing it from even entering the wormhole in the first place. This creates a paradox, but one that can be solved using mathematics. Two students studied this problem and found that from the same initial conditions there were many different trajectories the ball could take. For example, the ball might knock itself only slightly off course, resulting in it going it into the past slightly off course, which causes it to knock its past self only slightly off course, this trajectory then is completely consistent and causes no casualty violations, but the interesting thing is, there is more than one self consistent solution, in fact, there might even be an infinite amount of self consistent solutions. So, if we replace the billiard ball with a time traveller, then no matter what he wants to do, he will always end ! up accomplishing non paradoxical actions. I believe Darlton have used the self consistency principle to deal with the problems of time travel on the show and there is lots of evidence to support this.
Let’s start with Michael and the episode meet Kevin Johnson. During this episode it became clear that Michael couldn’t kill himself. The island, or destiny, just wouldn’t let him die, as shown by the scene where he tries to shoot himself and the gun miraculously jams. Later, Keamy attempts to kill him and his gun doesn’t work too, so i think its safe to assume that from the time Michael left the island, up until the time he died on the freighter, he was effectively immortal. The self consistency principle states this has to be case, he must live until this explosion or it would violate future casualty.
Michael has proven that by leaving the island on the correct bearing, fully conscious, a person will be immortal. This is why no-one is allowed to leave the island and also explains why Ben got so upset whenever anybody asked him.
Now that i think about it, there are just so many people immortal on this show. When Jin was on the freighter, he was immortal, since he had a self consistent future event in his life, so was Sayid and Desmond. In fact, Desmond was immortal from 1996, up until he had his time travel episodes. So, if he had tried to kill himself in 1999, he wouldn’t have been able too. This is because he had not yet learned Penny’s phone number for the self consistent future event on the freighter. This means the probability of Desmond dying in seasons 1 - 4 was zero.
In season 3, there was a plot line involving John Locke’s father appearing on the island so that Sawyer could kill him. According to Ben, it was Locke who brought his father to the island, now if we take Ben at his word, then Locke now has a self consistent event in his life, namely bringing his father to the island. The self consistency principle states that this has to happen and the probability of John Locke dying before this event actually occurs is zero, therefore at that time, although we didn’t know it, Locke was effectively immortal , in much the same way as Michael. This was proven when Ben shot Locke and left him for dead in the ditch, the bullet miraculously missed all his vital organs. More evidence can be found in cabin fever with the scene at the ditch, where Ben claims that shooting Locke was pointless.
Now I know what you’re all thinking, Locke couldn’t have been immortal since he is dead at this point and that event still hasn’t happened yet. There is however, two possible explanations. The first, evidence from Bens deleted scene that there was an extra Locke created the moment he turned the FDW, meaning he’s still alive and we’ll see him bring Cooper to the island at some point during season 6. Or the second explanation, and i haven’t properly checked this, is that its already happened. Remember when Locke left the island to bring them back, he was involved in a car wreck just after Abaddon was killed, what we didn’t see was Locke’s full trip from the cemetery to his eventual car crash, so it could be that he was involved in other incidents on route.
There is lots more evidence to support this theory, such as the pregnancy issues and the healing properties of the island, but this theory is already a bit lengthy so I’ll leave those for another time